Differential Topology: First Steps (Dover Books on Mathematics)
Contents:
So, I am encouraged by the other reviews of these books, particularly in Bloch, on Amazon, and among themselves: If you want to see his reviews, start with any of these four: He did not review either Milnor Morse Theory or Wallace. To find him, look under the reviews of Wallace.
Differential Topology: First Steps
So just what is differential topology? Seriously, it ought to be the study of differentiable manifolds smooth manifolds. But differential manifolds are, by intention, what we can do calculus on. And the calculus is a lot of machinery. And that was a lot of books.
Differential Topology: First Steps - Andrew H. Wallace - Google Книги
One way to think of differential topology is: Bloch says that geometric topology more narrowly defined would be topological and piecewise linear manifolds, but not differential. I think five of these six books can be characterized as: These books are going to discuss vector fields. Surely that counts as additional structure. The fact remains that these books look different from my differentiable manifolds books, which in turn look different from my differential geometry books.
Luca Signorelli rated it liked it Sep 30, First Steps Add to Wishlist. I think five of these six books can be characterized as: No trivia or quizzes yet. Mohammed Jhon marked it as to-read Apr 14, Can someone suggest me a good reference and prerequisites, if necessary,for studying above topics? Differential topology; first steps Andrew H.
I hope that as I add more books to the bibliography, I can make some sensible distinctions. I started out with 6 books in hand.
In the end, I stayed with the original 6, having seen no compelling reason to add or subtract from that list. Ah, one last point. Oh, another last point.
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A very little kid asked me what grade I was in in school, when I was a college freshman. I doubt that I will use either of those systems. Munkres is a reference book. Part II proves that every differentiable manifold has a unique smooth triangulation. Both Milnor Topology and Wallace cite this book. This self-contained treatment assumes only some knowledge of real numbers and real analysis.
Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more. Buy Differential Topology: First Steps (Dover Books on Mathematics) on Amazon. com ✓ FREE SHIPPING on qualified orders.
The first three chapters focus on the basics of point-set topology, after which the text proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. Exercises form an integral part of the text. Paperback , pages. To see what your friends thought of this book, please sign up. To ask other readers questions about An Introduction to Algebraic Topology , please sign up. Be the first to ask a question about An Introduction to Algebraic Topology.
Lists with This Book. This book is not yet featured on Listopia. Sep 06, CD rated it liked it Shelves: It was fun to hand Wallace to an earlier generation of Quantum Physicists who were not terribly familiar with AT and watch their eyes light up and then dim slightly if they hadn't ace'd Analysis in the Real Numbers or were vague on multi-dimensional Calc ala Ing or Sims.
Of course one day I started such a discussion and met a Candidate who had memorized all the solvable DiffEq's and knew what to do with them! That conversation lasted for many enjoyable years. I haven't seen the latest exercises guide so cannot speak for its efficacy as a text but this is gives a reader workable knowledge to unravel various applied work that supposes familiarity with the topic.
Chris Aldrich rated it really liked it May 29, Tu Analysis on Manifolds - James R.
An Introduction to Algebraic Topology
Munkres - expensive and hard to get. I'd recommend for a physicist. However I am loving: Introduction to Topological Manifolds - John M. Lee Topology - James R. Alec Teal 3, 1 19 Any questions about specifics please do ask. It seems that to read Lee's book or Tu's book, one should have good background in linear or abstract algebra to understand things such as homomorphism, dual vector space, field, etc.
Do you suggest any book for that?
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If you truly find yourself stuck on Tu, then I recommend the following two books to help out: A Unified Approach by Hubbard and Hubbard Both of these books should get you back on track regarding any missing material from your background. Other books to be aware of regarding supplemental material are: It is quite comprehensive, and there isn't a heavy emphasis from what I have read on proofs. Thus there are a ton of examples and applications. It's too quirky to use as your main learning source though, but it's great for supplemental insight.
Geometrical Vectors by Gabriel Weinreich - This is a very short but insightful read that would help put vectors, covectors, etc. Three other books on the subject that I am aware of but have no experience with: Curves - Surfaces - Manifolds by Wolfgang Kuhnel.